...solution; it ought to be practised by the beginner. Cor. From this example it is seen that a quantity may be transposed from one side of an equation to the other if its sign be chanyed. For if, instead of adding 5 to each side, we transpose the — 5, with its...

...19 12 12 V + -7 + -^ , th£t » 4 + 3 + 2, that is 9 ; o 4 b which agrees with the second side. 161. Any term may be transposed from one side of an equation to the other side by cftanging its sign. Suppose, for example, that x— a = by. Add a to each side ; then that...

...not French. Trans-pose, tram. роге', to change the order of [things]; (in Alg ) to change a term from one side of an equation to the other by changing its sign ; (in Music) to change the key; (in Gram.) to change the order of words or letters (contracted into...

...deduced a rule for facilitating the reduction of equations, that : — Any quantity may be removed from one side of an equation to the other by changing its sign. It is also manifest, that any quantity which is found on both sides of an equation may be expunged....

...called the root of the equation. To solve an equation is to find the root or roots. 48. Any quantity may be transposed from one side of an equation to the other by changing its signs. Thus, if x + 5 = 8 ; and 5 be subtracted from each side, then ая-5 — 6 = 8 — 5, or x —...

...an equation be multiplied or divided by the same quantity the results are equal. (ii) Any quantity may be transposed from one side of an equation to the other by changing its sign. (iii) If the sign of every term in an equation be changed the equality still holds. (iv) An equation...

...same as if b were transposed to the other side of the equation with its sign changed. Therefore, 115. Any term may be transposed from one side of an equation to the other provided its sign be changed. For, in this transposition, the same number is subtracted from each side...

...verified, or the equation satisfied, when, on substituting the value of the root in place of its symbol, the equation becomes identical. 171. The operations...Subtracting a from both members (Art. 171), we have x+a- a=b— a; or, by Art, 26, x = b — a, where + a has been transposed to the second member by ....

...same as if ¿ were transposed to the other side of the equation with its sign changed. Therefore, 114. Any term may be transposed from one side of an equation to the other provided its sign be changed. For, in this transposition, the same number is subtracted from each side...

...powers, or if like roots of the two members be taken, the results will be equal numbers (§ 18). 86. Any term may be transposed from one side of an equation to the other, provided its sign be changed. Suppose we have x + a = b. Now, a = a. Subtract, x = b — a. The a which...